low_rank_preconditioner_model Module Reference

Small algebraic helpers for the rotationally covariant low-rank OT preconditioner. More...

Functions/Subroutines
pure elemental real(kind=dp) function, public	low_rank_inverse_weight (eigenvalue, reference, energy_gap)
	Spectral inverse weight relative to a common occupied reference level.
pure integer function, public	low_rank_select_rank (eigenvalues, nocc, max_rank, degeneracy_tolerance)
	Select a bounded spectral rank without cutting a degenerate boundary manifold.
pure subroutine, public	apply_low_rank_dense (overlap_inverse, vectors, eigenvalues, reference, energy_gap, spectral_window, matrix_in, matrix_out)
	Dense reference application used to verify right covariance under orbital rotations.

Detailed Description

Small algebraic helpers for the rotationally covariant low-rank OT preconditioner.

Function/Subroutine Documentation

low_rank_inverse_weight()

pure elemental real(kind=dp) function, public low_rank_preconditioner_model::low_rank_inverse_weight	(	real(kind=dp), intent(in)	eigenvalue,
		real(kind=dp), intent(in)	reference,
		real(kind=dp), intent(in)	energy_gap )

Spectral inverse weight relative to a common occupied reference level.

Parameters

eigenvalue	complementary-state eigenvalue
reference	common occupied reference level
energy_gap	lower bound for the denominator

Returns

inverse spectral weight

Definition at line 28 of file low_rank_preconditioner_model.F.

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low_rank_select_rank()

pure integer function, public low_rank_preconditioner_model::low_rank_select_rank	(	real(kind=dp), dimension(:), intent(in)	eigenvalues,
		integer, intent(in)	nocc,
		integer, intent(in)	max_rank,
		real(kind=dp), intent(in)	degeneracy_tolerance )

Select a bounded spectral rank without cutting a degenerate boundary manifold.

Parameters

eigenvalues	ordered full-space eigenvalues
nocc	number of occupied states at the start of eigenvalues
max_rank	hard upper bound
degeneracy_tolerance	relative degeneracy threshold

Returns

selected rank

Definition at line 48 of file low_rank_preconditioner_model.F.

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apply_low_rank_dense()

pure subroutine, public low_rank_preconditioner_model::apply_low_rank_dense	(	real(kind=dp), dimension(:, :), intent(in)	overlap_inverse,
		real(kind=dp), dimension(:, :), intent(in)	vectors,
		real(kind=dp), dimension(:), intent(in)	eigenvalues,
		real(kind=dp), intent(in)	reference,
		real(kind=dp), intent(in)	energy_gap,
		real(kind=dp), intent(in)	spectral_window,
		real(kind=dp), dimension(:, :), intent(in)	matrix_in,
		real(kind=dp), dimension(:, :), intent(out)	matrix_out )

Dense reference application used to verify right covariance under orbital rotations.

Parameters

overlap_inverse	inverse overlap matrix
vectors	retained complementary-state vectors
eigenvalues	retained complementary-state eigenvalues
reference	common occupied reference level
energy_gap	lower bound for spectral denominators
spectral_window	overlap-inverse replacement window
matrix_in	input orbital-gradient matrix
matrix_out	preconditioned matrix

Definition at line 86 of file low_rank_preconditioner_model.F.

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